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Quantum Schur Sampling Circuits can be Strongly Simulated.

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Researchers developed a classical algorithm to efficiently approximate transition amplitudes in permutational quantum computing (PQC). This addresses a key challenge, demonstrating classical tractability for certain PQC computations.

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Area of Science:

  • Quantum Information Science
  • Computational Complexity Theory
  • Quantum Computing

Background:

  • Permutational quantum computing (PQC) is a natural quantum computational model.
  • PQC is conjectured to capture nonclassical aspects of quantum computation.
  • Estimating matrix elements of S_n irreducible representation matrices in Young's orthogonal form was a known computational challenge.

Purpose of the Study:

  • To investigate the classical tractability of estimating transition amplitudes in PQC.
  • To develop an efficient classical algorithm for approximating these transition amplitudes.
  • To extend the findings to a broader class of quantum circuits.

Main Methods:

  • Development of a novel classical algorithm for approximation.
  • Analysis of transition amplitudes for PQC circuits.
  • Extension of the method to quantum Schur sampling circuits.

Main Results:

  • An efficient classical algorithm is presented to approximate PQC transition amplitudes with polynomial additive precision.
  • This algorithm solves a previously intractable problem for classical computation.
  • The method is extended to efficiently approximate transition amplitudes for quantum Schur sampling circuits.

Conclusions:

  • The conjecture that estimating PQC transition amplitudes is classically intractable is disproven.
  • Efficient classical approximation of PQC transition amplitudes is achievable.
  • This work broadens the understanding of the relationship between quantum and classical computational power.